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Simple & Compound Interest

SI, CI, half-yearly compounding and the difference between them.

42 solved questions · 14 easy · 19 medium · 9 hard

Take a 10-question quiz on Simple & Compound Interest, no login

Shortcuts & formulas

  • Simple interest: SI = P x R x T/100 (T in years); Amount = P + SI.
  • Compound interest: A = P(1 + R/100)^n; CI = A - P. Half-yearly: rate R/2, periods 2n. Quarterly: rate R/4, periods 4n.
  • Difference between CI and SI for 2 years = P(R/100)^2; for 3 years = P(R/100)^2 x (300 + R)/100.
  • At SI, a sum becomes k times itself in T years at rate R when R x T = 100(k - 1).
  • Rate of CI from two consecutive amounts: R% = (A(n+1) - A(n))/A(n) x 100.
  • For a time in days, use T = days/365 years; for months, T = months/12.
  • Equal annual instalments at CI: Loan = x/(1+r) + x/(1+r)^2 + ... (discount each instalment back).

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

Find the simple interest on ₹5,000 at 8% per annum for 3 years.

  1. A₹1,200
  2. B₹1,000
  3. C₹1,500
  4. D₹1,400
Show answer & solution

Answer: A. ₹1,200

Solution

SI = PRT/100 = 5,000 x 8 x 3/100 = ₹1,200 Answer: ₹1,200

Q2.

What amount will ₹12,000 become in 2 years at 6% simple interest per annum?

  1. A₹1,440
  2. B₹13,200
  3. C₹13,236
  4. D₹13,440
Show answer & solution

Answer: D. ₹13,440

Solution

SI = 12,000 x 6 x 2/100 = ₹1,440 Amount = 12,000 + 1,440 = ₹13,440 Answer: ₹13,440

Q3.

At what rate per annum will ₹8,000 earn ₹1,920 as simple interest in 3 years?

  1. A6%
  2. B12%
  3. C8%
  4. D10%
Show answer & solution

Answer: C. 8%

Solution

R = SI x 100/(P x T) = 1,920 x 100/(8,000 x 3) = 8% Answer: 8%

Q4.

In how many years will ₹6,000 earn ₹1,800 as simple interest at 5% per annum?

  1. A5 years
  2. B6 years
  3. C4 years
  4. D3 years
Show answer & solution

Answer: B. 6 years

Solution

T = SI x 100/(P x R) = 1,800 x 100/(6,000 x 5) = 6 years Answer: 6 years

Q5.

What sum of money earns ₹900 simple interest in 2 years at 7.5% per annum?

  1. A₹6,000
  2. B₹5,000
  3. C₹7,000
  4. D₹6,500
Show answer & solution

Answer: A. ₹6,000

Solution

P = SI x 100/(R x T) = 900 x 100/(7.5 x 2) = ₹6,000 Answer: ₹6,000

Q6.

Find the compound interest on ₹10,000 for 2 years at 10% per annum, compounded annually.

  1. A₹2,000
  2. B₹2,200
  3. C₹1,000
  4. D₹2,100
Show answer & solution

Answer: D. ₹2,100

Solution

Amount = 10,000 x (1.1)^2 = 12,100 CI = 12,100 - 10,000 = ₹2,100 Answer: ₹2,100

Q7.

What is the amount if ₹8,000 is invested for 2 years at 5% per annum compound interest?

  1. A₹8,800
  2. B₹9,620
  3. C₹8,820
  4. D₹8,200
Show answer & solution

Answer: C. ₹8,820

Solution

A = 8,000 x (1.05)^2 = 8,000 x 1.1025 = ₹8,820 Answer: ₹8,820

Q8.

Find the difference between the compound interest and simple interest on ₹10,000 for 2 years at 10% per annum.

  1. A₹1,000
  2. B₹100
  3. C₹10
  4. D₹200
Show answer & solution

Answer: B. ₹100

Solution

Difference for 2 years = P(R/100)^2 = 10,000 x (0.1)^2 = ₹100 Answer: ₹100

Shortcut: SI = 2,000, CI = 2,100, so the difference is 100.

Q9.

A sum doubles itself in 8 years at simple interest. What is the rate per annum?

  1. A12.5%
  2. B8%
  3. C10%
  4. D12%
Show answer & solution

Answer: A. 12.5%

Solution

Interest = Principal in 8 years R x 8 = 100 R = 12.5% Answer: 12.5%

Q10.

Simple interest on a sum for 4 years at 5% is ₹1,500. Find the sum.

  1. A₹6,000
  2. B₹3,000
  3. C₹9,000
  4. D₹7,500
Show answer & solution

Answer: D. ₹7,500

Solution

P = 1,500 x 100/(5 x 4) = ₹7,500 Answer: ₹7,500

Q11.

A sum amounts to ₹6,600 in 2 years at 10% simple interest. What is the sum?

  1. A₹5,000
  2. B₹6,000
  3. C₹5,500
  4. D₹5,940
Show answer & solution

Answer: C. ₹5,500

Solution

A = P(1 + RT/100) = P x 1.2 P = 6,600/1.2 = ₹5,500 Answer: ₹5,500

Q12.

Find the simple interest on ₹1,00,000 at 10% per annum for 73 days.

  1. A₹1,000
  2. B₹2,000
  3. C₹7,300
  4. D₹2,500
Show answer & solution

Answer: B. ₹2,000

Solution

T = 73/365 = 0.2 year SI = 1,00,000 x 10 x 0.2/100 = ₹2,000 Answer: ₹2,000

Q13.

At 4% simple interest per annum, what is the interest on ₹25,000 for 6 months?

  1. A₹500
  2. B₹1,000
  3. C₹250
  4. D₹5,000
Show answer & solution

Answer: A. ₹500

Solution

T = 6/12 = 0.5 year SI = 25,000 x 4 x 0.5/100 = ₹500 Answer: ₹500

Q14.

₹2,000 becomes ₹2,420 in 2 years at compound interest. What is the rate per annum?

  1. A21%
  2. B11%
  3. C20%
  4. D10%
Show answer & solution

Answer: D. 10%

Solution

(1 + R/100)^2 = 2,420/2,000 = 1.21 1 + R/100 = 1.1 R = 10% Answer: 10%

Medium questions

Q15.

Find the compound interest on ₹16,000 for 1 year at 20% per annum, compounded half-yearly.

  1. A₹3,200
  2. B₹3,520
  3. C₹3,360
  4. D₹3,300
Show answer & solution

Answer: C. ₹3,360

Solution

Half-yearly: rate = 10% per half-year, periods = 2 A = 16,000 x (1.1)^2 = 19,360 CI = 19,360 - 16,000 = ₹3,360 Answer: ₹3,360

Q16.

Find the amount on ₹10,000 for 1 year at 8% per annum compounded quarterly.

  1. A₹10,800
  2. B₹10,824.32
  3. C₹10,816
  4. D₹10,824
Show answer & solution

Answer: B. ₹10,824.32

Solution

Quarterly rate = 2%, periods = 4 A = 10,000 x (1.02)^4 = 10,000 x 1.08243216 = ₹10,824.32 Answer: ₹10,824.32

Q17.

A sum of ₹15,000 is invested at 10% per annum compound interest, compounded annually. What is the compound interest after 3 years?

  1. A₹4,965
  2. B₹4,500
  3. C₹5,000
  4. D₹4,800
Show answer & solution

Answer: A. ₹4,965

Solution

A = 15,000 x (1.1)^3 = 15,000 x 1.331 = 19,965 CI = 19,965 - 15,000 = ₹4,965 Answer: ₹4,965

Q18.

Find the difference between compound interest and simple interest on ₹20,000 for 3 years at 5% per annum.

  1. A₹150
  2. B₹500
  3. C₹1,000
  4. D₹152.50
Show answer & solution

Answer: D. ₹152.50

Solution

SI = 20,000 x 5 x 3/100 = ₹3,000 A = 20,000 x (1.05)^3 = 23,152.50, so CI = ₹3,152.50 Difference = 3,152.50 - 3,000 = ₹152.50 Answer: ₹152.50

Q19.

The compound interest on a sum for 2 years at 10% per annum is ₹1,050. What is the sum?

  1. A₹4,500
  2. B₹5,250
  3. C₹5,000
  4. D₹10,500
Show answer & solution

Answer: C. ₹5,000

Solution

CI factor for 2 years at 10% = 1.21 - 1 = 0.21 P = 1,050/0.21 = ₹5,000 Answer: ₹5,000

Q20.

The difference between CI and SI on a sum for 2 years at 8% per annum is ₹48. Find the sum.

  1. A₹6,000
  2. B₹7,500
  3. C₹7,000
  4. D₹8,000
Show answer & solution

Answer: B. ₹7,500

Solution

Difference = P(R/100)^2 48 = P x (0.08)^2 = P x 0.0064 P = 48/0.0064 = ₹7,500 Answer: ₹7,500

Q21.

In how many years will a sum triple itself at 12.5% simple interest per annum?

  1. A16 years
  2. B8 years
  3. C12 years
  4. D20 years
Show answer & solution

Answer: A. 16 years

Solution

Interest = 2 x Principal R x T = 200 T = 200/12.5 = 16 years Answer: 16 years

Q22.

A sum at compound interest becomes 4 times itself in 2 years. What is the annual rate of interest?

  1. A50%
  2. B200%
  3. C75%
  4. D100%
Show answer & solution

Answer: D. 100%

Solution

(1 + R/100)^2 = 4 1 + R/100 = 2 R = 100% Answer: 100%

Q23.

A man lends ₹12,000, part at 6% and the rest at 9% simple interest per annum. His yearly income is ₹900. How much is lent at 9%?

  1. A₹4,000
  2. B₹8,000
  3. C₹6,000
  4. D₹5,000
Show answer & solution

Answer: C. ₹6,000

Solution

Let amount at 9% = x 0.06(12,000 - x) + 0.09x = 900 720 + 0.03x = 900 x = 180/0.03 = ₹6,000 Answer: ₹6,000

Q24.

Asha borrows ₹20,000 at 6% simple interest per annum and lends it at 8% per annum. What is her gain in 3 years?

  1. A₹4,800
  2. B₹1,200
  3. C₹3,600
  4. D₹2,400
Show answer & solution

Answer: B. ₹1,200

Solution

Gain rate = 8% - 6% = 2% per year Gain = 20,000 x 2 x 3/100 = ₹1,200 Answer: ₹1,200

Q25.

A sum of ₹5,000 is invested for 2 years at 10% compound interest in the first year and 20% in the second year. What is the amount?

  1. A₹6,600
  2. B₹6,500
  3. C₹6,720
  4. D₹6,000
Show answer & solution

Answer: A. ₹6,600

Solution

After year 1: 5,000 x 1.10 = 5,500 After year 2: 5,500 x 1.20 = 6,600 Answer: ₹6,600

Q26.

The population of a town is 1,25,000 and grows 8% every year (compounded). What is it after 2 years?

  1. A1,45,000
  2. B1,40,000
  3. C1,44,000
  4. D1,45,800
Show answer & solution

Answer: D. 1,45,800

Solution

After 1 year: 1,25,000 x 1.08 = 1,35,000 After 2 years: 1,35,000 x 1.08 = 1,45,800 Answer: 1,45,800

Q27.

The simple interest on a sum for 2 years at 5% per annum is ₹500. What is the compound interest on the same sum for the same time and rate?

  1. A₹500
  2. B₹525
  3. C₹512.50
  4. D₹510
Show answer & solution

Answer: C. ₹512.50

Solution

SI = P x 5 x 2/100 = 500, so P = ₹5,000 A = 5,000 x (1.05)^2 = 5,512.50 CI = ₹512.50 Answer: ₹512.50

Q28.

A sum of money at simple interest amounts to ₹1,200 in 2 years and ₹1,350 in 3 years. What is the sum?

  1. A₹1,000
  2. B₹900
  3. C₹800
  4. D₹750
Show answer & solution

Answer: B. ₹900

Solution

Interest for 1 year = 1,350 - 1,200 = ₹150 Interest for 2 years = ₹300 Sum = 1,200 - 300 = ₹900 Answer: ₹900

Q29.

At what rate of compound interest per annum will ₹4,000 amount to ₹4,840 in 2 years?

  1. A10%
  2. B21%
  3. C11%
  4. D20%
Show answer & solution

Answer: A. 10%

Solution

(1 + R/100)^2 = 4,840/4,000 = 1.21 1 + R/100 = 1.1 R = 10% Answer: 10%

Q30.

How much more does ₹10,000 earn in 2 years at 20% per annum compounded half-yearly than compounded annually?

  1. A₹200
  2. B₹410
  3. C₹141
  4. D₹241
Show answer & solution

Answer: D. ₹241

Solution

Annually: 10,000 x (1.2)^2 = 14,400 Half-yearly: 10% for 4 periods, 10,000 x (1.1)^4 = 14,641 Difference = 14,641 - 14,400 = ₹241 Answer: ₹241

Q31.

₹2,500 is lent at 12% simple interest per annum. After how many months will the interest be ₹150?

  1. A3 months
  2. B12 months
  3. C6 months
  4. D5 months
Show answer & solution

Answer: C. 6 months

Solution

T = SI x 100/(P x R) = 150 x 100/(2,500 x 12) = 0.5 year = 6 months Answer: 6 months

Q32.

A sum of ₹8,000 amounts to ₹9,261 in 3 years at compound interest. Find the rate per annum.

  1. A4%
  2. B5%
  3. C6%
  4. D10%
Show answer & solution

Answer: B. 5%

Solution

(1 + R/100)^3 = 9,261/8,000 = 1.157625 1.05^3 = 1.157625, so R = 5% Answer: 5%

Q33.

A machine worth ₹1,00,000 loses 10% of its value every year. What is its value after 2 years?

  1. A₹80,000
  2. B₹90,000
  3. C₹81,000
  4. D₹81,500
Show answer & solution

Answer: C. ₹81,000

Solution

After year 1: 1,00,000 x 0.90 = 90,000 After year 2: 90,000 x 0.90 = 81,000 Answer: ₹81,000

Hard questions

Q34.

A sum becomes ₹5,832 in 2 years and ₹6,298.56 in 3 years at compound interest. Find the sum.

  1. A₹5,000
  2. B₹4,800
  3. C₹5,200
  4. D₹4,900
Show answer & solution

Answer: A. ₹5,000

Solution

Rate = (6,298.56 - 5,832)/5,832 x 100 = 466.56/5,832 x 100 = 8% P x (1.08)^2 = 5,832 P = 5,832/1.1664 = ₹5,000 Answer: ₹5,000

Q35.

A loan of ₹21,000 at 10% per annum compound interest is to be repaid in two equal annual instalments. Find each instalment.

  1. A₹10,500
  2. B₹11,000
  3. C₹12,600
  4. D₹12,100
Show answer & solution

Answer: D. ₹12,100

Solution

Let each instalment be x x/1.1 + x/1.21 = 21,000 x(1.1 + 1)/1.21 = 21,000 x = 21,000 x 1.21/2.1 = ₹12,100 Answer: ₹12,100

Q36.

A sum of ₹3,600 is lent at R% simple interest for R years and earns ₹900 in all. Find R.

  1. A4%
  2. B5%
  3. C6%
  4. D10%
Show answer & solution

Answer: B. 5%

Solution

SI = P x R x R/100 = 3,600 R^2/100 = 36 R^2 36 R^2 = 900 R^2 = 25, R = 5% Answer: 5%

Q37.

At simple interest a sum becomes 3 times itself in 12 years. In how many years will it become 5 times itself?

  1. A24 years
  2. B20 years
  3. C36 years
  4. D30 years
Show answer & solution

Answer: A. 24 years

Solution

Interest = 2P in 12 years, so interest = P in 6 years For 5 times, interest = 4P = 4 x 6 = 24 years Answer: 24 years

Q38.

A sum of money doubles itself in 5 years at compound interest. In how many years will it become 8 times itself?

  1. A20 years
  2. B40 years
  3. C25 years
  4. D15 years
Show answer & solution

Answer: D. 15 years

Solution

Doubling every 5 years: 2 -> 4 -> 8 takes 3 doubling periods Time = 3 x 5 = 15 years Answer: 15 years

Q39.

Find the amount on ₹15,000 for 3 years 4 months at 10% per annum, where compound interest is applied for the full years and simple interest for the remaining months.

  1. A₹19,965
  2. B₹20,000
  3. C₹20,630.50
  4. D₹20,330.50
Show answer & solution

Answer: C. ₹20,630.50

Solution

After 3 years: 15,000 x (1.1)^3 = ₹19,965 SI on 19,965 for 4 months (1/3 year) = 19,965 x 10 x (1/3)/100 = ₹665.50 Amount = 19,965 + 665.50 = ₹20,630.50 Answer: ₹20,630.50

Q40.

For a sum, the simple interest for 2 years is ₹1,200 and the compound interest for 2 years is ₹1,260. Find the sum.

  1. A₹5,000
  2. B₹6,000
  3. C₹6,500
  4. D₹7,200
Show answer & solution

Answer: B. ₹6,000

Solution

SI for 1 year = 600; CI - SI = 60 = SI for 1 year x R/100 60 = 600 x R/100, so R = 10% SI for 2 years = P x 10 x 2/100 = 1,200 P = ₹6,000 Answer: ₹6,000

Q41.

₹9,000 is divided into two parts. The first is lent at 6% simple interest for 2 years and the second at 8% for 3 years, and both earn equal interest. Find the first part.

  1. A₹6,000
  2. B₹3,000
  3. C₹4,500
  4. D₹5,000
Show answer & solution

Answer: A. ₹6,000

Solution

Let first = x, second = 9,000 - x x x 6 x 2/100 = (9,000 - x) x 8 x 3/100 12x = 24(9,000 - x) 36x = 2,16,000 x = ₹6,000 Answer: ₹6,000

Q42.

Find the compound interest on ₹8,000 for 1 year 6 months at 20% per annum compounded half-yearly.

  1. A₹2,400
  2. B₹2,640
  3. C₹2,800
  4. D₹2,648
Show answer & solution

Answer: D. ₹2,648

Solution

Rate per half-year = 10%, periods = 3 A = 8,000 x (1.1)^3 = 8,000 x 1.331 = 10,648 CI = 10,648 - 8,000 = ₹2,648 Answer: ₹2,648

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